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MIT 18.02SC Multivariable Calculus, Fall 2010

by: MIT OpenCourseWare

Publication date: 2010

Usage: Attribution-Noncommercial-Share Alike 3.0

Topics: multivariable calculus, vectors, matrices, partial derivatives, double integrals, line integrals, triple integrals, surface integrals

Language: English

Instructor: Christine Breiner, David Jordan, Joel Lewis

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

View the complete course: http://ocw.mit.edu/18-02SCF10

Addeddate: 2011-01-04 14:17:04

Color: color

Identifier: MIT18_02SCF10

Sound: sound

Year: 2010

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47,998 Views

10 Favorites

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47.7M

Coordinate free proofs: centroid of a triangle

37.2M

Dot products and angles

21.7M

Components of a vector

14.5M

Area of a parallelogram

20.0M

12.5M

Volume of a parallelepiped

21.6M

Finding area using cross products

45.3M

Matrix multiplication practice

76.9M

Solve a linear system using matrices

58.8M

Equations of planes

35.1M

Distance of a point to a plane

51.0M

Systems of linear equations

36.4M

Parametrized lines and intersections

34.4M

Parametric line intersecting a plane

59.8M

Differentiating a vector valued function

35.4M

Parametric curves: velocity, acceleration, length

33.4M

Graphing surfaces

44.3M

35.7M

Level curves and critical points

22.6M

Partial derivatives

29.4M

Tangent plane approximation

38.5M

36.8M

Second derivative test

59.5M

Max/Min

49.2M

Total differentials and the chain rule

38.4M

57.7M

Gradient and directional derivative

43.6M

Lagrange multipliers

56.4M

Lagrange multipliers (3 variables)

65.0M

The chain rule with constraints

43.9M

Gradients - composition

75.7M

Regions of integration

25.8M

Changing the order of integration

74.8M

Integration in polar coordinates

66.2M

Integrals with density

39.2M

Change of variables

40.7M

Integral of exp(-x^2)

84.7M

Change of variables

66.1M

Line integrals: path dependence

53.3M

Line integrals: parametrization independence

44.9M

Line integrals by geometric reasoning

47.3M

Fundamental theorem of line integrals

42.5M

Non-conservative vector fields

48.3M

Potentials of gradient fields

31.9M

Green's Theorem: an off center circle

36.3M

Green's Theorem: area under an arch

30.6M

Application of Green's theorem

61.3M

Flux across a curve

46.9M

Green's Theorem in normal form

99.2M

Extended Green's Theorem

58.2M

Domains of vector fields

77.0M

Volume in cylindrical coordinates

62.2M

42.4M

Moment of inertia of a cylinder

55.1M

Average distance on a sphere

47.8M

Gravity and a half-sphere

28.8M

Flux through easy surfaces

42.6M

Flux through a square

48.2M

Flux through surfaces

48.0M

Flux

50.9M

Flux and the divergence theorem

80.4M

Extended Gauss' Theorem

36.0M

Del and the product rule

47.8M

Line integral on a helix

63.2M

Conservative fields and exact differentials

74.7M

Stokes' Theorem

66.5M

Extended Stokes' Theorem

62.9M

Simply connected regions

35.4M

More Stokes' Theorem

47.8M

Consequences of Stokes' Theorem

ITEM TILE

MPEG4

24.8M

Coordinate free proofs: centroid of a triangle

19.3M

Dot products and angles

11.3M

Components of a vector

7.5M

Area of a parallelogram

10.4M

6.5M

Volume of a parallelepiped

11.1M

Finding area using cross products

23.7M

Matrix multiplication practice

40.0M

Solve a linear system using matrices

30.7M

Equations of planes

18.2M

Distance of a point to a plane

26.5M

Systems of linear equations

18.8M

Parametrized lines and intersections

17.8M

Parametric line intersecting a plane

31.2M

Differentiating a vector valued function

18.5M

Parametric curves: velocity, acceleration, length

17.2M

Graphing surfaces

23.1M

18.6M

Level curves and critical points

11.7M

Partial derivatives

15.3M

Tangent plane approximation

20.0M

19.1M

Second derivative test

30.9M

Max/Min

25.5M

Total differentials and the chain rule

19.9M

30.0M

Gradient and directional derivative

22.7M

Lagrange multipliers

29.4M

Lagrange multipliers (3 variables)

33.7M

The chain rule with constraints

22.9M

Gradients - composition

39.2M

Regions of integration

13.4M

Changing the order of integration

38.8M

Integration in polar coordinates

34.5M

Integrals with density

20.5M

Change of variables

21.1M

Integral of exp(-x^2)

44.3M

Change of variables

34.1M

Line integrals: path dependence

27.5M

Line integrals: parametrization independence

23.4M

Line integrals by geometric reasoning

24.7M

Fundamental theorem of line integrals

22.1M

Non-conservative vector fields

25.2M

Potentials of gradient fields

16.6M

Green's Theorem: an off center circle

19.0M

Green's Theorem: area under an arch

16.1M

Application of Green's theorem

31.8M

Flux across a curve

24.3M

Green's Theorem in normal form

51.8M

Extended Green's Theorem

30.3M

Domains of vector fields

39.7M

Volume in cylindrical coordinates

32.4M

22.1M

Moment of inertia of a cylinder

28.7M

Average distance on a sphere

24.9M

Gravity and a half-sphere

14.9M

Flux through easy surfaces

22.2M

Flux through a square

25.0M

Flux through surfaces

25.1M

Flux

26.6M

Flux and the divergence theorem

42.0M

Extended Gauss' Theorem

18.8M

Del and the product rule

25.0M

Line integral on a helix

33.0M

Conservative fields and exact differentials

39.0M

Stokes' Theorem

34.8M

Extended Stokes' Theorem

32.9M

Simply connected regions

18.5M

More Stokes' Theorem

24.9M

Consequences of Stokes' Theorem

48.5M

Coordinate free proofs: centroid of a triangle

37.8M

Dot products and angles

22.0M

Components of a vector

14.6M

Area of a parallelogram

20.2M

12.4M

Volume of a parallelepiped

21.6M

Finding area using cross products

45.8M

Matrix multiplication practice

77.3M

Solve a linear system using matrices

59.7M

Equations of planes

35.6M

Distance of a point to a plane

51.7M

Systems of linear equations

36.3M

Parametrized lines and intersections

34.4M

Parametric line intersecting a plane

60.1M

Differentiating a vector valued function

35.6M

Parametric curves: velocity, acceleration, length

33.4M

Graphing surfaces

44.4M

35.7M

Level curves and critical points

22.6M

Partial derivatives

29.6M

Tangent plane approximation

38.8M

37.3M

Second derivative test

60.2M

Max/Min

49.2M

Total differentials and the chain rule

38.8M

58.5M

Gradient and directional derivative

44.1M

Lagrange multipliers

57.2M

Lagrange multipliers (3 variables)

64.9M

The chain rule with constraints

44.2M

Gradients - composition

76.6M

Regions of integration

25.7M

Changing the order of integration

74.8M

Integration in polar coordinates

66.3M

Integrals with density

39.7M

Change of variables

40.9M

Integral of exp(-x^2)

85.3M

Change of variables

66.1M

Line integrals: path dependence

53.3M

Line integrals: parametrization independence

45.7M

Line integrals by geometric reasoning

47.3M

Fundamental theorem of line integrals

42.9M

Non-conservative vector fields

48.5M

Potentials of gradient fields

32.2M

Green's Theorem: an off center circle

36.9M

Green's Theorem: area under an arch

30.9M

Application of Green's theorem

61.8M

Flux across a curve

47.7M

Green's Theorem in normal form

99.9M

Extended Green's Theorem

58.4M

Domains of vector fields

77.2M

Volume in cylindrical coordinates

63.3M

43.1M

Moment of inertia of a cylinder

55.6M

Average distance on a sphere

48.0M

Gravity and a half-sphere

29.0M

Flux through easy surfaces

42.6M

Flux through a square

48.6M

Flux through surfaces

48.8M

Flux

51.7M

Flux and the divergence theorem

81.3M

Extended Gauss' Theorem

36.3M

Del and the product rule

47.9M

Line integral on a helix

63.6M

Conservative fields and exact differentials

75.5M

Stokes' Theorem

67.3M

Extended Stokes' Theorem

63.3M

Simply connected regions

35.7M

More Stokes' Theorem

48.2M

Consequences of Stokes' Theorem

SUBRIP

16.1K

Coordinate free proofs: centroid of a triangle

11.6K

Dot products and angles

6.5K

Components of a vector

3.9K

Area of a parallelogram

5.2K

3.5K

Volume of a parallelepiped

5.7K

Finding area using cross products

15.8K

Matrix multiplication practice

31.4K

Solve a linear system using matrices

21.4K

Equations of planes

11.3K

Distance of a point to a plane

16.2K

Systems of linear equations

10.8K

Parametrized lines and intersections

9.4K

Parametric line intersecting a plane

24.3K

Differentiating a vector valued function

12.4K

Parametric curves: velocity, acceleration, length

9.7K

Graphing surfaces

12.3K

11.0K

Level curves and critical points

6.8K

Partial derivatives

10.3K

Tangent plane approximation

14.7K

12.0K

Second derivative test

19.1K

Max/Min

13.9K

Total differentials and the chain rule

11.5K

17.9K

Gradient and directional derivative

13.9K

Lagrange multipliers

20.0K

Lagrange multipliers (3 variables)

18.9K

The chain rule with constraints

11.7K

Gradients - composition

27.9K

Regions of integration

7.0K

Changing the order of integration

20.0K

Integration in polar coordinates

17.2K

Integrals with density

14.4K

Change of variables

15.7K

Integral of exp(-x^2)

30.2K

Change of variables

20.0K

Line integrals: path dependence

16.4K

Line integrals: parametrization independence

15.4K

Line integrals by geometric reasoning

11.8K

Fundamental theorem of line integrals

16.5K

Non-conservative vector fields

16.0K

Potentials of gradient fields

11.4K

Green's Theorem: an off center circle

13.5K

Green's Theorem: area under an arch

10.3K

Application of Green's theorem

23.4K

Flux across a curve

14.9K

Green's Theorem in normal form

37.6K

Extended Green's Theorem

21.1K

Domains of vector fields

26.2K

Volume in cylindrical coordinates

21.7K

14.1K

Moment of inertia of a cylinder

19.3K

Average distance on a sphere

18.6K

Gravity and a half-sphere

10.8K

Flux through easy surfaces

13.9K

Flux through a square

17.3K

Flux through surfaces

15.7K

Flux

17.7K

Flux and the divergence theorem

27.4K

Extended Gauss' Theorem

12.9K

Del and the product rule

17.3K

Line integral on a helix

22.2K

Conservative fields and exact differentials

25.8K

Stokes' Theorem

21.3K

Extended Stokes' Theorem

24.4K

Simply connected regions

10.6K

More Stokes' Theorem

15.9K

Consequences of Stokes' Theorem

TORRENT

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